An effective 3-D finite element scheme for computing electromagnetic field distortions due to defects in eddy-current nondestructive evaluation

A Perturbation Method for the 3D Finite Element Modeling of Electrostatically Driven MEMS

“…Particularizing (1a-b-c) for both the unperturbed and perturbed problems, we obtain [8] curl e u = 0, div…”

“…with the field perturbations [8]: e = e p − e u and d = d p − d u . Note that if ε p = ε u , an additional source term given by the unperturbed solution (ε p − ε u ) e u is considered in (6c).…”

“…An unperturbed problem is first defined in Ω without considering the properties of a so-called perturbing region Ω c,p which will further lead to field distortions [8][9] [10]. At the discrete level, this region is not described in the mesh of Ω.…”

“…Mesh of Ω (1); distribution of the unperturbed electric potential v u (2) and electrice field e u (3); adapted mesh of Ω p (4); distribution of the perturbation electric potential v (5) and the perturbed one v p (6); distribution of the perturbation electric field e (7) and the perturbed one e p (8) For each iteration i (i = 0, 1, ...), we determine the electric scalar potential v 2i in Ω, with v 0 = v u . The projection of this solution from its original mesh to that of the added conductor Ω c,p gives a source v s,2i+1 for a perturbation problem.…”

“…An unperturbed problem is first solved in a large mesh taking advantage of any symmetry and excluding additional regions and thus avoiding their mesh. Its solution is applied as a source to the further computations of the perturbed problems when conductive regions are added [8][9] [10]. It benefits from the use of different subproblem-adapted meshes, this way the computational efficiency increases as the size of each sub-problem diminishes [9].…”